I figured it was something to do with "Windows Live One Care". I disabled scanning and firewall, quite Retrospect (necessary), restarted Retrospect, and it found the clients. I then re-enabled everything, but Retrospect could still find the clients. (I did incidentally enable "Network Discovery" in Live One Care -- it had been disabled, but I didn't expect that to make much difference).

So I don't know what's wrong. I'm hoping it's not some odd effect of my relatively new gigabit switch.